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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"contentcontainer med left\" style=\"margin-left: -50px;\">\n",
    "<dl class=\"dl-horizontal\">\n",
    "  <dt>Title</dt> <dd> QuadMesh Element</dd>\n",
    "  <dt>Dependencies</dt> <dd>Bokeh</dd>\n",
    "  <dt>Backends</dt> <dd><a href='./QuadMesh.ipynb'>Bokeh</a></dd> <dd><a href='../matplotlib/QuadMesh.ipynb'>Matplotlib</a></dd>\n",
    "</dl>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import holoviews as hv\n",
    "hv.extension('bokeh')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The basic ``QuadMesh`` is a 2D grid of bins specified as x-/y-values specifying a regular sampling or edges, with arbitrary sampling and an associated 2D array containing the bin values. Here is a simple ``QuadMesh`` with logarithmic sampling along the 'x' dimensions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 8  # Number of bins in each direction\n",
    "xs = np.logspace(1, 3, n)\n",
    "ys = np.linspace(1, 10, n)\n",
    "zs = np.arange((n-1)**2).reshape(n-1, n-1)\n",
    "hv.QuadMesh((xs, ys, zs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coordinate system of a ``QuadMesh`` is defined by the bin edges, therefore any index falling into a binned region will return the appropriate value. ``QuadMesh`` supports inspection of values using the Bokeh hover tools and because the bin edges have continuous values, you can use non-linear axes such as log axes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%opts QuadMesh [tools=['hover'] xticks=[10, 100,1000]] QuadMesh.LogScale [logx=True]\n",
    "hv.QuadMesh((xs, ys, zs), group='LinearScale') + hv.QuadMesh((xs, ys, zs), group='LogScale')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unlike ``Image`` objects, slices must be inclusive of the bin edges but otherwise the slicing semantics are the same. The reason for this difference is that ``QuadMesh`` is really a two-dimensional histogram and when slicing, you only want to see the bins that fall within the specified slice ranges.\n",
    "\n",
    "In the next example, we specify a slice along the x- and y-axis to extract the lower corner and we set the z-dimension range to maintain the full color range of the colormap:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "qmesh = hv.QuadMesh((xs, ys, zs))\n",
    "qmesh[20:400, :8].redim.range(z=qmesh.range('z'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As ``QuadMesh`` supports the Bokeh hover tool while ``Image`` does not, we can get use a simple trick to enable hover information: overlay the image with an invisible ``QuadMesh`` cast from the same image. We can set the ``QuadMesh`` alpha to zero while keeping an opaque hover line color:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%opts QuadMesh [tools=['hover']] (alpha=0 hover_line_alpha=1 hover_line_color='black')\n",
    "img = hv.Image(np.random.rand(10,10))\n",
    "img * hv.QuadMesh(img)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now when you hover over this visualization, you can see the sample value as well as an outline of the selected bin."
   ]
  }
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